Xiong Jincheng, Sets of Recurrent Points of Continuous Maps of the Interval, Proceedings of the American Mathematical Society, Vol. 95, No. 3 (Nov., 1985), pp. 491-494 ...

We prove the result stated in the title; that is, every separable Banach space is linearly isometric to a closed subspace E of the space of continuous functions on [ 0, 1 ], such that every nonzero ...